On 8/22/07, bob koca <[EMAIL PROTECTED]> wrote: > > > > > > In money games, one can expect from doubling theory that with perfect > play, > > 2/3 of initial doubles are takes (for redoubles, it is 1/2). Simulations > > with GNUBG 2-ply playing against itself indeed get very close to this > > number. > > > > Do your 2/3 and 1/2 figures come from early-late ratios? >
One could see this as the result from the application of these early/late ratios I suppose. I don't see the jump from the ratios > to the statement that those fractions of doubles are takes. Could you > explain please? > You're probably looking for a mathematical proof or something, which I haven't seen yet. I can only say that for me it seems intuitively sort of clear that these early/late ratios will lead to these take/pass ratios (at least approximately), under the assumption that equity and equity change distributions in backgammon are not too skewed (and maybe other assumptions as well). GNUBG 2-ply simulations support the idea that 2/3 and 1/2 are (approximately) the right numbers, which for me is quite convincing as far as real life backgammon is concerned. This subject was discussed on GOL once, and from what I remember there was consensus about this relation beween early/late and pass/take ratios. If anyone knows of a more theoretical approach to this problem or comes up with different ratios, I'd be interested in it. -- Robert-Jan Veldhuizen (Zorba on FIBS)
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